Why do Horde races want to be in the horde?

It is a sign of respect for the high king position. He is not high king because he is not a king. Having said that, high king and Supreme Commander are of equal rank and power, just different titles/honorifics.

So far it seems like we have “Supreme Allied Commander” “high King” “Lord Commander” of the Alliance all occupying the same rank/have the same power.

My mistake. They apperently only mention his official title. Lord Commander.